distfit is a Python package for probability density fitting of univariate distributions for random variables. The distfit library can determine the best fit for over 90 theoretical distributions. The goodness-of-fit test is used to score for the best fit and after finding the best-fitted theoretical distribution, the loc, scale, and arg parameters are returned. It can be used for parametric, non-parametric, and discrete distributions. ⭐️Star it if you like it⭐️

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Key Features

Feature	Description
Parametric Fitting	Fit distributions on empirical data X.
Non-Parametric Fitting	Fit distributions on empirical data X using non-parametric approaches (quantile, percentiles).
Discrete Fitting	Fit distributions on empirical data X using binomial distribution.
Predict	Compute probabilities for response variables y.
Synthetic Data	Generate synthetic data.
Plots	Varoius plotting functionalities.

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Resources and Links

• Example Notebooks: Examples
• Blog Posts: Medium
• Documentation: Website
• Bug Reports and Feature Requests: GitHub Issues

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Background

• For the parametric approach, The distfit library can determine the best fit across 89 theoretical distributions. To score the fit, one of the scoring statistics for the good-of-fitness test can be used used, such as RSS/SSE, Wasserstein, Kolmogorov-Smirnov (KS), or Energy. After finding the best-fitted theoretical distribution, the loc, scale, and arg parameters are returned, such as mean and standard deviation for normal distribution.

• For the non-parametric approach, the distfit library contains two methods, the quantile and percentile method. Both methods assume that the data does not follow a specific probability distribution. In the case of the quantile method, the quantiles of the data are modeled whereas for the percentile method, the percentiles are modeled.

• In case the dataset contains discrete values, the distift library contains the option for discrete fitting. The best fit is then derived using the binomial distribution.

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Installation

Install distfit from PyPI

pip install distfit

Install from Github source

pip install git+https://github.com/erdogant/distfit

Imort Library

import distfit
print(distfit.__version__)

# Import library
from distfit import distfit

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Examples

Example: Quick start to find best fit for your input data

# [distfit] >INFO> fit
# [distfit] >INFO> transform
# [distfit] >INFO> [norm      ] [0.00 sec] [RSS: 0.00108326] [loc=-0.048 scale=1.997]
# [distfit] >INFO> [expon     ] [0.00 sec] [RSS: 0.404237] [loc=-6.897 scale=6.849]
# [distfit] >INFO> [pareto    ] [0.00 sec] [RSS: 0.404237] [loc=-536870918.897 scale=536870912.000]
# [distfit] >INFO> [dweibull  ] [0.06 sec] [RSS: 0.0115552] [loc=-0.031 scale=1.722]
# [distfit] >INFO> [t         ] [0.59 sec] [RSS: 0.00108349] [loc=-0.048 scale=1.997]
# [distfit] >INFO> [genextreme] [0.17 sec] [RSS: 0.00300806] [loc=-0.806 scale=1.979]
# [distfit] >INFO> [gamma     ] [0.05 sec] [RSS: 0.00108459] [loc=-1862.903 scale=0.002]
# [distfit] >INFO> [lognorm   ] [0.32 sec] [RSS: 0.00121597] [loc=-110.597 scale=110.530]
# [distfit] >INFO> [beta      ] [0.10 sec] [RSS: 0.00105629] [loc=-16.364 scale=32.869]
# [distfit] >INFO> [uniform   ] [0.00 sec] [RSS: 0.287339] [loc=-6.897 scale=14.437]
# [distfit] >INFO> [loggamma  ] [0.12 sec] [RSS: 0.00109042] [loc=-370.746 scale=55.722]
# [distfit] >INFO> Compute confidence intervals [parametric]
# [distfit] >INFO> Compute significance for 9 samples.
# [distfit] >INFO> Multiple test correction method applied: [fdr_bh].
# [distfit] >INFO> Create PDF plot for the parametric method.
# [distfit] >INFO> Mark 5 significant regions
# [distfit] >INFO> Estimated distribution: beta [loc:-16.364265, scale:32.868811]

Example: Plot summary of the tested distributions

After we have a fitted model, we can make some predictions using the theoretical distributions. After making some predictions, we can plot again but now the predictions are automatically included.

Example: Make predictions using the fitted distribution

Example: Test for one specific distributions

The full list of distributions is listed here: https://erdogant.github.io/distfit/pages/html/Parametric.html

Example: Test for multiple distributions

The full list of distributions is listed here: https://erdogant.github.io/distfit/pages/html/Parametric.html

Example: Fit discrete distribution

from scipy.stats import binom
# Generate random numbers

# Set parameters for the test-case
n = 8
p = 0.5

# Generate 10000 samples of the distribution of (n, p)
X = binom(n, p).rvs(10000)
print(X)

# [5 1 4 5 5 6 2 4 6 5 4 4 4 7 3 4 4 2 3 3 4 4 5 1 3 2 7 4 5 2 3 4 3 3 2 3 5
#  4 6 7 6 2 4 3 3 5 3 5 3 4 4 4 7 5 4 5 3 4 3 3 4 3 3 6 3 3 5 4 4 2 3 2 5 7
#  5 4 8 3 4 3 5 4 3 5 5 2 5 6 7 4 5 5 5 4 4 3 4 5 6 2...]

# Import distfit
from distfit import distfit

# Initialize for discrete distribution fitting
dfit = distfit(method='discrete')

# Run distfit to and determine whether we can find the parameters from the data.
dfit.fit_transform(X)

# [distfit] >fit..
# [distfit] >transform..
# [distfit] >Fit using binomial distribution..
# [distfit] >[binomial] [SSE: 7.79] [n: 8] [p: 0.499959] [chi^2: 1.11]
# [distfit] >Compute confidence interval [discrete]

Example: Make predictions on unseen data for discrete distribution

Example: Generate samples based on the fitted distribution

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Contributors

Setting up and maintaining bnlearn has been possible thanks to users and contributors. Thanks to:

Maintainer

• Erdogan Taskesen, github: erdogant
• Contributions are welcome.
• Yes! This library is entirely free but it runs on coffee! :) Feel free to support with a Coffee.